PrerequisitesPrerequisite

Solving by completing the square - irrational real solutions

Find two real, irrational solutions and leave them in simplified radical form.

  • Complete the square and isolate the squared parenthesis.
  • Take both square roots. A positive non-square leaves a radical.
  • Simplify the radical and keep the answers exact rather than rounding to decimals.

Example 1

Solve by completing the square. Give exact answers.

Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.

Example 2

Solve by completing the square. Give exact answers.

Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.

Remember
For example, . The symbol represents two different real answers.

Your turn

Question 1

Solve by completing the square. Give exact answers.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.
Question 2

Solve by completing the square. Give exact answers.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.
Question 3

Solve by completing the square. Give exact answers.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.
Question 4

Solve by completing the square. Give exact answers.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.
Question 5

Solve by completing the square. Give exact answers.

Check answer
Halve to get ; subtract its square.Simplify the numerical terms and collect like terms.
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